Question

In a triangle ABC, the sides are $6$ cm, $10$ cm and $14$ cm. What is the measure of the obtuse angle?

• A. ${120}^o$
• B. ${135}^o$
• C. ${150}^o$
• D. ${165}^o$

Answer 1

The correct option is A ${120}^o$

Cosine rule of triangle
$\cos C=\frac{a^2+b^2-c^2}{2ab}$
$\therefore$ large angle is opposite to long side
$\therefore \cos A=\frac{6^2+{10}^2-{14}^2}{2\times 6\times 10}=\frac{136-196}{2\times 60}=\frac{-60}{2\times 60}$
$\cos A=\frac{-1}{2}$
$A={120}^0$